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Label Polynomial Discriminant Galois group Class group
32.0.24788700386255228556692600250244140625.1 x32 - 2x31 + x29 + 14x28 - 23x27 - 25x26 + 77x25 + 32x24 - 233x23 + 130x22 + 275x21 - 204x20 - 500x19 + 369x18 + 976x17 - 775x16 - 1988x15 + 2706x14 + 1255x13 - 4074x12 + 870x11 + 3435x10 - 2784x9 - 528x8 + 1624x7 - 465x6 - 564x5 + 639x4 - 293x3 + 55x2 - x + 1 \( 5^{28}\cdot 13^{16} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.47330370277129322496000000000000000000000000.1 x32 + x28 - x20 - x16 - x12 + x4 + 1 \( 2^{64}\cdot 3^{16}\cdot 5^{24} \) $C_2^3\times C_4$ (as 32T34) $[4]$ (GRH)
32.0.352701833122210710593389803720131611763844129.1 x32 - x31 + x29 - x28 + x26 - x25 + x23 - x22 + x20 - x19 + x17 - x16 + x15 - x13 + x12 - x10 + x9 - x7 + x6 - x4 + x3 - x + 1 \( 3^{16}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[5]$ (GRH)
32.0.515207889456069254383620937908064472169867121.1 x32 - 5x31 + 22x30 - 73x29 + 220x28 - 519x27 + 1255x26 - 2247x25 + 4413x24 - 6238x23 + 9744x22 - 10830x21 + 13240x20 - 10628x19 + 12053x18 - 5501x17 + 12591x16 - 3062x15 + 17256x14 + 194x13 + 18165x12 + 5659x11 + 13232x10 - 2318x9 - 319x8 - 13445x7 - 6940x6 - 4990x5 + 1466x4 + 2074x3 + 1626x2 + 264x + 79 \( 7^{16}\cdot 13^{28} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.4722366482869645213696000000000000000000000000.1 x32 - x24 + x16 - x8 + 1 \( 2^{96}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[5]$ (GRH)
32.0.14648040110065267094876580444599852735215435776.1 x32 - x16 + 1 \( 2^{128}\cdot 3^{16} \) $C_2^2\times C_8$ (as 32T37) $[3, 3]$ (GRH)
32.0.35190667333271321019306672876612934335729762304.1 x32 - x30 + x28 - x26 + x24 - x22 + x20 - x18 + x16 - x14 + x12 - x10 + x8 - x6 + x4 - x2 + 1 \( 2^{32}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[8]$ (GRH)
32.0.366225584701948244050176000000000000000000000000.1 x32 - 3x30 + 4x28 - 9x26 + 27x24 - 93x22 + 188x20 - 279x18 + 581x16 - 1116x14 + 3008x12 - 5952x10 + 6912x8 - 9216x6 + 16384x4 - 49152x2 + 65536 \( 2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.520402924666472696020370152488960000000000000000.1 x32 - 47x24 + 2208x16 - 47x8 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{16} \) $C_2^3\times C_4$ (as 32T34) $[20]$ (GRH)
32.0.1250223652010309685753479160887484565582275390625.1 x32 - x31 + 2x30 - 3x29 + 5x28 - 8x27 + 13x26 - 21x25 + 34x24 - 55x23 + 89x22 - 144x21 + 233x20 - 377x19 + 610x18 - 987x17 + 1597x16 + 987x15 + 610x14 + 377x13 + 233x12 + 144x11 + 89x10 + 55x9 + 34x8 + 21x7 + 13x6 + 8x5 + 5x4 + 3x3 + 2x2 + x + 1 \( 5^{16}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[17]$ (GRH)
32.0.1461501637330902918203684832716283019655932542976.1 x32 + 1 \( 2^{160} \) $C_2\times C_{16}$ (as 32T32) $[17]$ (GRH)
32.2.1478570811461626154162295475745342334411977277407.1 x32 - x - 1 \( -\,191\cdot 19329543076986451\cdot 400485847292917407445603765627 \) $S_{32}$ (as 32T2801324) Trivial (GRH)
32.0.2294081869728198830572049522437155246734619140625.1 x32 - 11x31 + 68x30 - 336x29 + 1315x28 - 4335x27 + 12498x26 - 30713x25 + 67152x24 - 127199x23 + 211471x22 - 307078x21 + 387026x20 - 419617x19 + 359728x18 - 149755x17 - 229142x16 + 581095x15 - 441722x14 - 315448x13 + 1021466x12 - 946897x11 + 366311x10 - 50246x9 + 132237x8 - 215882x7 + 157773x6 - 97500x5 + 79930x4 - 54894x3 + 25063x2 - 7709x + 3131 \( 3^{32}\cdot 5^{28}\cdot 7^{16} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.6142666889587199870339155304469168186187744140625.1 x32 - 4x31 + 38x30 - 130x29 + 699x28 - 2191x27 + 8745x26 - 25571x25 + 83386x24 - 222738x23 + 612551x22 - 1445800x21 + 3366820x20 - 6839883x19 + 13440516x18 - 23161945x17 + 38310126x16 - 55684805x15 + 77474162x14 - 94829103x13 + 110710129x12 - 113727761x11 + 110357640x10 - 94103904x9 + 74479117x8 - 51698016x7 + 32429638x6 - 17496051x5 + 7973462x4 - 3036857x3 + 868340x2 - 166271x + 16531 \( 5^{28}\cdot 67^{16} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.36539993586348786372837376000000000000000000000000.1 x32 - x28 - 15x24 + 31x20 + 209x16 + 496x12 - 3840x8 - 4096x4 + 65536 \( 2^{64}\cdot 5^{24}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.51922968585348276285304963292200960000000000000000.1 x32 + 2207x16 + 1 \( 2^{128}\cdot 5^{16} \) $C_2^2\times C_8$ (as 32T37) $[17]$ (GRH)
32.0.113341328678310292663197722067951895712000278265856.1 x32 + 31x24 + 705x16 + 7936x8 + 65536 \( 2^{96}\cdot 3^{16}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) $[4, 4, 4]$ (GRH)
32.0.272292877590407567597186433188495333554574218609249.1 x32 - x31 - x30 + 3x29 - x28 - 5x27 + 7x26 + 3x25 - 17x24 + 11x23 + 23x22 - 45x21 - x20 + 91x19 - 89x18 - 93x17 + 271x16 - 186x15 - 356x14 + 728x13 - 16x12 - 1440x11 + 1472x10 + 1408x9 - 4352x8 + 1536x7 + 7168x6 - 10240x5 - 4096x4 + 24576x3 - 16384x2 - 32768x + 65536 \( 7^{16}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[3, 15]$ (GRH)
32.0.506364211574415072751124736000000000000000000000000.1 x32 - 5x30 + 9x28 - 10x26 + 50x24 - 565x22 + 1746x20 - 1130x18 - 911x16 - 10170x14 + 141426x12 - 411885x10 + 328050x8 - 590490x6 + 4782969x4 - 23914845x2 + 43046721 \( 2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 11^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.794071845499378503449051136000000000000000000000000.1 x32 - 4x30 + 2x28 + 40x26 - 160x24 + 544x22 - 264x20 - 5440x18 + 21744x16 - 10880x14 - 1056x12 + 4352x10 - 2560x8 + 1280x6 + 128x4 - 512x2 + 256 \( 2^{88}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[5, 20]$ (GRH)
32.0.794071845499378503449051136000000000000000000000000.2 x32 + 4x30 + 2x28 - 40x26 - 160x24 - 544x22 - 264x20 + 5440x18 + 21744x16 + 10880x14 - 1056x12 - 4352x10 - 2560x8 - 1280x6 + 128x4 + 512x2 + 256 \( 2^{88}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[4, 8]$ (GRH)
32.0.1392709810786878646248924865118341505527496337890625.1 x32 - x31 + 2x30 - 13x29 + 20x28 - 18x27 + 134x26 - 237x25 + 228x24 - 1272x23 + 1343x22 - 1297x21 + 9166x20 - 10201x19 + 1484x18 - 39009x17 + 47769x16 + 118245x15 + 50069x14 + 29982x13 + 25190x12 + 81350x11 + 89951x10 + 32414x9 + 26164x8 + 15519x7 + 32913x6 + 37152x5 + 13527x4 + 6318x3 + 4374x2 + 8748x + 6561 \( 3^{16}\cdot 5^{24}\cdot 13^{24} \) $C_2\times C_4^2$ (as 32T36) $[104]$ (GRH)
32.0.1689856796077948861582881651286068022251129150390625.1 x32 - x31 + 8x30 - 9x29 + 44x28 - 38x27 + 192x26 - 145x25 + 766x24 - 556x23 + 2257x22 - 1493x21 + 5640x20 - 2513x19 + 11628x18 - 4801x17 + 21029x16 - 8919x15 + 26197x14 - 7798x13 + 27196x12 - 90x11 + 19367x10 - 2094x9 + 12428x8 - 3657x7 + 3055x6 - 664x5 + 741x4 + 134x3 + 26x2 + 4x + 1 \( 5^{24}\cdot 17^{28} \) $C_4\times C_8$ (as 32T43) $[365]$ (GRH)
32.0.2306255574353269294321282113641705264626385702354944.1 x32 - 2x30 + 4x28 - 8x26 + 16x24 - 32x22 + 64x20 - 128x18 + 256x16 - 512x14 + 1024x12 - 2048x10 + 4096x8 - 8192x6 + 16384x4 - 32768x2 + 65536 \( 2^{48}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[3, 24]$ (GRH)
32.0.2306255574353269294321282113641705264626385702354944.2 x32 + 2x30 + 4x28 + 8x26 + 16x24 + 32x22 + 64x20 + 128x18 + 256x16 + 512x14 + 1024x12 + 2048x10 + 4096x8 + 8192x6 + 16384x4 + 32768x2 + 65536 \( 2^{48}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) n/a
32.0.4026692887688564776141139207792885760000000000000000.1 x32 - 7x28 - 704x24 - 5047x20 + 565969x16 - 80752x12 - 180224x8 - 28672x4 + 65536 \( 2^{64}\cdot 3^{16}\cdot 5^{16}\cdot 7^{16} \) $C_2^5$ (as 32T39) n/a
32.0.5241670721450327242974152113348873388724842246701056.1 x32 - 15x30 + 134x28 - 793x26 + 3496x24 - 11638x22 + 30241x20 - 60672x18 + 94862x16 - 111861x14 + 99380x12 - 61666x10 + 26973x8 - 6636x6 + 1086x4 - 36x2 + 1 \( 2^{32}\cdot 3^{16}\cdot 17^{28} \) $C_2^2\times C_8$ (as 32T37) $[40]$ (GRH)
32.0.7332864799814241410137948416000000000000000000000000.1 x32 + 7x30 + 9x28 - 154x26 - 1078x24 - 5593x22 - 6462x20 + 123046x18 + 854761x16 + 1107414x14 - 523422x12 - 4077297x10 - 7072758x8 - 9093546x6 + 4782969x4 + 33480783x2 + 43046721 \( 2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 13^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.11308580273943039971119355619759072515285051093549056.1 x32 + 449x16 + 65536 \( 2^{128}\cdot 7^{16} \) $C_2^2\times C_8$ (as 32T37) $[136]$ (GRH)
32.0.24000959919026880122072334336000000000000000000000000.1 x32 - 2x31 + 9x30 - 30x29 + 46x28 + 64x27 - 323x26 + 2264x25 - 7635x24 + 21504x23 - 30305x22 + 57880x21 + 39466x20 - 694266x19 + 2319339x18 - 3485698x17 + 14846451x16 - 12810752x15 + 2519526x14 + 3448824x13 - 3068744x12 + 1256816x11 - 39944x10 - 329952x9 + 240720x8 - 70592x7 - 12128x6 + 24320x5 - 13184x4 + 3072x3 + 1152x2 - 1024x + 256 \( 2^{48}\cdot 3^{16}\cdot 5^{24}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.24000959919026880122072334336000000000000000000000000.2 x32 - 2x31 + x30 - 10x29 - 20x28 - 136x27 + 489x26 + 412x25 + 1455x24 - 380x23 + 20765x22 - 113020x21 + 22444x20 - 71630x19 + 273805x18 - 1917530x17 + 8820755x16 - 6803856x15 - 3050102x14 + 14422848x13 - 16249472x12 + 4718368x11 + 18224552x10 - 33044576x9 + 20240880x8 + 9340480x7 + 2473504x6 + 461696x5 - 5632x4 + 15872x3 + 6272x2 + 1536x + 256 \( 2^{48}\cdot 3^{16}\cdot 5^{24}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.50522262278163705147147943936000000000000000000000000.1 x32 - 7x28 - 32x24 + 791x20 - 2945x16 + 64071x12 - 209952x8 - 3720087x4 + 43046721 \( 2^{64}\cdot 5^{24}\cdot 11^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.138956997215838851269528412416000000000000000000000000.1 x32 + 3x30 - 9x28 - 85x26 - 114x24 - 1521x22 - 2090x20 + 22329x18 + 111717x16 - 44722x14 - 41235x12 + 33462x10 + 16051x8 + 13275x6 - 11826x4 - 2916x2 + 6561 \( 2^{32}\cdot 5^{24}\cdot 13^{24} \) $C_2\times C_4^2$ (as 32T36) $[4, 4, 4]$ (GRH)
32.0.156712132992285501115475016655592096377279059345801216.1 x32 + 113x24 + 6208x16 + 741393x8 + 43046721 \( 2^{96}\cdot 3^{16}\cdot 11^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.170615961014359235699341036323165930807590484619140625.1 x32 - 9x31 + 200x29 - 221x28 - 2631x27 + 4402x26 + 19766x25 - 27449x24 - 173128x23 + 338537x22 + 473336x21 - 1004401x20 - 3368948x19 + 11453717x18 - 8139429x17 - 16834230x16 - 597015x15 + 195460786x14 - 382818671x13 - 27697040x12 + 420160443x11 + 1322753872x10 - 3917503795x9 + 2111159122x8 + 2050419221x7 + 1497324960x6 - 10922257252x5 + 11658561303x4 - 2839464368x3 - 2153549419x2 + 711827200x + 313809121 \( 5^{28}\cdot 127^{16} \) $C_8.A_4$ (as 32T402) $[3]$ (GRH)
32.0.186221552718646678775874367536462493032617340087890625.1 x32 - x31 + 23x30 - 12x29 + 329x28 - 122x27 + 2779x26 - 327x25 + 16520x24 - 338x23 + 64543x22 + 7650x21 + 180555x20 + 24855x19 + 346044x18 + 50946x17 + 490499x16 + 64136x15 + 494181x14 + 64009x13 + 369102x12 + 46478x11 + 187873x10 + 28296x9 + 67299x8 + 9995x7 + 13558x6 + 2674x5 + 1791x4 + 184x3 + 62x2 - 4x + 1 \( 3^{16}\cdot 5^{16}\cdot 17^{28} \) $C_2^2\times C_8$ (as 32T37) $[2040]$ (GRH)
32.0.203282392447840896882957090816000000000000000000000000.1 x32 - 16x30 + 152x28 - 960x26 + 4525x24 - 16184x22 + 45376x20 - 98960x18 + 169224x16 - 220120x14 + 215964x12 - 146912x10 + 67325x8 - 13840x6 + 1988x4 - 48x2 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[2, 2, 20]$ (GRH)
32.32.203282392447840896882957090816000000000000000000000000.1 x32 - 32x30 + 464x28 - 4032x26 + 23401x24 - 95704x22 + 283612x20 - 616816x18 + 986442x16 - 1151648x14 + 965328x12 - 564928x10 + 220856x8 - 53696x6 + 7136x4 - 384x2 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) Trivial (GRH)
32.0.203282392447840896882957090816000000000000000000000000.2 x32 - 8x30 + 44x28 - 208x26 + 911x24 - 2776x22 + 7272x20 - 17024x18 + 34257x16 - 47152x14 + 59688x12 - 65552x10 + 50831x8 - 3464x6 + 236x4 - 16x2 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[2, 2, 20]$ (GRH)
32.0.203282392447840896882957090816000000000000000000000000.3 x32 + 269x24 + 5886x16 + 1124x8 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[2, 10, 20]$ (GRH)
32.0.203282392447840896882957090816000000000000000000000000.4 x32 + 349x24 + 30126x16 + 274084x8 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[8, 16]$ (GRH)
32.0.203282392447840896882957090816000000000000000000000000.5 x32 + 8x30 + 44x28 + 208x26 + 911x24 + 2776x22 + 7272x20 + 17024x18 + 34257x16 + 47152x14 + 59688x12 + 65552x10 + 50831x8 + 3464x6 + 236x4 + 16x2 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[8, 80]$ (GRH)
32.0.203282392447840896882957090816000000000000000000000000.6 x32 + 16x30 + 152x28 + 960x26 + 4525x24 + 16184x22 + 45376x20 + 98960x18 + 169224x16 + 220120x14 + 215964x12 + 146912x10 + 67325x8 + 13840x6 + 1988x4 + 48x2 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[4, 8, 80]$ (GRH)
32.0.203282392447840896882957090816000000000000000000000000.7 x32 + 32x30 + 464x28 + 4032x26 + 23401x24 + 95704x22 + 283612x20 + 616816x18 + 986442x16 + 1151648x14 + 965328x12 + 564928x10 + 220856x8 + 53696x6 + 7136x4 + 384x2 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[40, 80]$ (GRH)
32.0.203282392447840896882957090816000000000000000000000000.8 x32 - 175x24 + 30000x16 - 109375x8 + 390625 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.203282392447840896882957090816000000000000000000000000.9 x32 - 81x24 + 6561x16 - 531441x8 + 43046721 \( 2^{96}\cdot 3^{16}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) n/a
32.0.210183365271596281474544229277581939111301912914296832.1 x32 - 3x16 + 3 \( 2^{128}\cdot 3^{31} \) 32T22195 Trivial (GRH)
32.0.357097144070652207046431305343854464590549468994140625.1 x32 + 10x30 - 34x29 - 221x28 - 325x27 + 1702x26 + 10506x25 + 30252x24 + 14963x23 - 179369x22 - 807831x21 - 1736093x20 - 816295x19 + 9325990x18 + 44064917x17 + 128084070x16 + 284677470x15 + 521805347x14 + 810649893x13 + 1086373418x12 + 1261930239x11 + 1284857142x10 + 1126974132x9 + 881072238x8 + 561801072x7 + 341439909x6 + 154026757x5 + 83319621x4 + 32957519x3 + 18318673x2 + 5994407x + 1916071 \( 5^{28}\cdot 7^{16}\cdot 19^{16} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.376487536747625684443481098520430035050561572415862689.1 x32 - x31 - 2x30 + 5x29 + x28 - 16x27 + 13x26 + 35x25 - 74x24 - 31x23 + 253x22 - 160x21 - 599x20 + 1079x19 + 718x18 - 3955x17 + 1801x16 - 11865x15 + 6462x14 + 29133x13 - 48519x12 - 38880x11 + 184437x10 - 67797x9 - 485514x8 + 688905x7 + 767637x6 - 2834352x5 + 531441x4 + 7971615x3 - 9565938x2 - 14348907x + 43046721 \( 11^{16}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) n/a
32.0.401761478270509541172805101174925557760000000000000000.1 x32 - 1457x24 + 565953x16 - 372992x8 + 65536 \( 2^{96}\cdot 5^{16}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) $[2, 8, 8]$ (GRH)

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